## Statistical Quality Control

Statistical Quality Control

Assignment: Please read the material (Fundamentals of Quality Control and Improvement) and use the book to answers all questions as followed.

Note: Questions are from Exercise and Problem of Fundamentals of Quality Control and Improvement.

Question 1 (Chapter 4):

A local hospital estimates that the number of patients admitted daily to the emergency room has a Poisson probability distribution with a mean of 4.0. What is the probability that on a given day

a) only 3 patients will be admitted?

b) at most 8 patients will be admitted?

c) no one will be admitted?

d) For each patient admitted, the expected daily operational expenses to the hospital are $600. If the hospital wants to be 94.1% sure of meeting daily expenses, how much money should it retain for operational expenses daily?

Question 2 (Chapter 4):

The specifications for the thickness of nonferrous washers are 1.0 +/- 0.04 mm. From the process data, the distribution of the washer thickness is estimated to be normal with a mean of 0.97 mm and a standard deviation of 0.02 mm. The unit cost of rework is $0.10, and the unit cost of scrap is $0.15. For a daily production of 10,000 items:

a) What proportion of the washers is conforming? What is the total daily cost of rework and scrap?

b) In its study of constant improvement, the manufacturer changes the mean setting of the machine to 1.0 mm. If the standard deviation is the same as before, what is the total daily cost of rework and scrap?

c) The manufacturer is trying to further improve on the process and reduces its standard deviation to 0.015 mm. If

the process mean is maintained at 1.0 mm, what is the percent decrease in the total daily cost of rework and scrap compared to that of part (a)?

Question 3 (Chapter 4):

The time to repair an equipment is known to be exponentially distributed with a mean of 45min.

(a) What is the probability of the machine being repaired within half an hour?

(b) If the machine breaks down at 3P.M. and a repairman is available immediately, what is the probability of the machine being available for production by the start of the next day? Assume that the repairman is available until 5P.M.

(c) If there are two machines being repaired, what is the probability that both machines will not be available within the next 50 minutes?

Question 4 (Chapter 4, exercise 4-4):

Explain the difference between accuracy and precision of measurements. How do you control for accuracy? What can you do about precision?

Question 5 (Chapter 4, exercise 4-11):

Consider the price of homes in a large metropolitan area. What kind of distribution would you expect in terms of skewness and kurtosis? As an index, would the mean or median price be representative? What would the interquartile range indicate?